Filtering in the Time and Frequency Domains
This book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships.
TABLE OF CONTENTS Filtering in the Time and Frequency Domains
3.7: SPECIAL CASES
3.7 SPECIAL CASES
We now briefly examine filter responses derived from other considerations, including the transitional responses, which attempt to compromise between good delay and good attenuation; responses obtained by placing transfer-function poles on specific contours; the age-old synchronous response, and the magnitude response with equiripple passband and stopband behavior (Cauer filter).
3.7.1 Transitional Responses
Transitional responses are a compromise between constant passband delay and a rectangular magnitude response. From the ideal response analysis of Section 3.1.12 we know that constant passband delay requires a rounded passband attenuation function, whereas stopband behavior does not appreciably influence the delay. This fact is translated into two filter classes: the Butterworth-Thomson and the Gaussian-Chebyshev.
The first class [15] is obtained by mating the maximally flat magnitude and group delay approximations. The transfer-function poles incorporate a parameter m that is adjustable from 0 to 1. For m = 0, the Butterworth response is obtained and the Thomson response is found for m = 1. Intermediate values of m give responses whose characteristics lie somewhere between these two extremes. Transfer function poles for this class are given in Ref. 23 for n = 2 to n = 10, as well as 15 values of m for each value of n.
The second class [10] is a Gaussian approximation in a Chebyshev manner over a specified frequency interval after which the attenuation increases rapidly, characteristic of Chebyshev responses. Data for the Gaussian approximations to the 6 and to the...
Copyright Herman J. Blinchikoff 2001 under license agreement with Books24x7
